Question

Oснова ВС трапеції ABCD лежить в площині а. Вершина D не належить площині а. Пряму l побудовано через середини бічних сторін трапеції. Доведіть, що l || а. Побудуйте рисунок до завдання.​

Answer 1

Task Analysis and Diagram Construction

To prove that the line l is parallel to the plane a, we can use the fact that l passes through the midpoints of the non-parallel sides of the trapezoid ABCD. Let's construct a diagram to visualize the given information and aid in the proof.

Proof of l || a

Given: - Trapezoid ABCD lies in plane a. - Vertex D does not belong to plane a. - Line l is constructed through the midpoints of the non-parallel sides of the trapezoid.

To prove: l is parallel to plane a.

Proof: 1. Let M and N be the midpoints of the non-parallel sides AB and CD, respectively. 2. Consider the line segment MN, which lies in the plane a. 3. Since line l passes through the midpoint of MN, it also lies in the plane a. 4. Therefore, line l is parallel to plane a.

Diagram Construction

I'm sorry, but as a text-based AI model, I'm unable to create visual diagrams. However, you can visualize the trapezoid ABCD with the line l passing through the midpoints of the non-parallel sides AB and CD, and the plane a containing the trapezoid.

If you have any further questions or need additional assistance, feel free to ask!